You appear to have successfully added the Settings App to your Dock. As for why you are unable to move items to and from the Dock, as I described, I cannot fathom. The described method works without difficulty on my library of Apple devices - each currently running iPadOS 12/15/17/18.x.
Presumably you refer to moving the Settings App icon from the Home Screen to the Dock seen at the bottom of your screenshot. You simply need to drag the Settings App icon to the Dock...
Touch and hold the settings icon. When the icons wobble, simply drag the Settings icon to the dock - and then lift your finger from the screen. Finally, tap any empty area of the Home Screen to finish moving icons.
Should you need additional information, the iPad User Guide is a rich source of information about your iPad and iPadOS. Here is a direct link to the relevant section of the Guide:
Move apps and widgets on the iPad Home Screen - Apple Support
No. I have another page of apps. I just went into Settings>>Home Screen & App Library. I clicked on Show App Library in Dock. Then I went to the Home Screen and moved the mail app and settings app to the left of the / partition. Next I went back to the Settings and unchecked the Show App Library in Dock. Went back to the Home Screen and the mail app, Safari app and Settings app are now in the dock. I wish your s and user guide would work- it would be simpler. Thank you for your help.
I used your suggestion and user guide link and after I dragged the settings app to the dock it pops right back up to its original place. I tried moving the mail app off the dock and tried to move it on the dock and it popped back to the Home Screen.
Your screenshot shows very few App icons. Are you using a "managed" iPad - perhaps in an Educational or Enterprise environment?
I’m not using a managed iPad nor educational or enterprise environment. Just my own personal new iPad. I have mor apps on another page.
And a third page of apps. Plus those only in the App Library.
ipad mini A17: On the home screen- how do you move the settings app to the bottom box next to the safari app.?